Abstract
We investigate Scattering amplitudes of the reversible $\theta$-exact Seiberg-Witten (SW) map based noncommutative (NC) quantum electrodynamics, and show explicitly the SW map invariance for all tree-level NCQED $2\to2$ proceses, including M\"oller, Bhabha, Compton, pair annihilation, pair production and light-by-light $(\gamma\gamma\to\gamma\gamma)$ scatterings. We apply our NCQED results to the $\gamma\gamma\to\gamma\gamma$ and $\gamma\gamma\to\ell^+\ell^-$ exclusive processes, convoluted to the ultraperipheral lead $^{208}$Pb ion-ion collisions, recently measured by the ATLAS collaboration at LHC. We demonstrate that $\gamma\gamma\to\gamma\gamma$ is the more appropriate channel to probe NC scale $\Lambda_{\rm NC}$ while both are less efficient than some other probes.
Highlights
Lorentz symmetry, as a cornerstone of modern physics, appears with the Einstein formulation of the special theory of relativity in 1905
In the modern string theory framework regarding the effect of spontaneous breaking of Lorentz symmetry, one of the most striking observations is that via tensor field vacuum expectation values the low-energy effective theory can be expressed by usual gauge fields or gauge fields deformed by space-time noncommutativity (NC)
After taking into account two identical particles in the final state, we have obtained for arbitrary energies in the NCM frame the following pure NCQED exclusive cross section σγNC2 : 4Because of the similarity or complementarity of NCQED with QCD, there exist only three maximal helicity violating (MHV) independent noncommutative amplitudes ðþþþþ; þþ−−; þ−þ−Þ given in Eq (92)
Summary
As a cornerstone of modern physics, appears with the Einstein formulation of the special theory of relativity in 1905. We fill this vacancy by demonstrating explicitly that all tree-level two-by-two scattering amplitudes in an NCQED model defined with a reversible θ-exact SW map are identical to their unmapped counterparts, which is compatible with the formal equivalence proven before [130,131,132] As applications of this newly found identity, we revisit the NCQED two-by-two processes and, in particular, lightby-light scatterings and lepton pair production processes in the context of ATLAS ultraperipheral lead 208Pb ion-ion collision measurements [133,134,135,136] and show that LbyL scattering is a better probe to the NC scale of these two. For relevant integrals and other mathematical issues among Wolfram Mathematica [150], we are using mainly Gradshteyn and Ryzhik [151]
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